# Learning Generative Models across Incomparable Spaces

arXiv: https://arxiv.org/abs/1905.05461 · HTML: https://mlsanity.com/paper/1905.05461/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 30 of 53)

- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs](https://mlsanity.com/paper/2106.01128/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [3D Pose Transfer with Correspondence Learning and Mesh Refinement](https://mlsanity.com/paper/2109.15025/) (2021)
- [Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embedding](https://mlsanity.com/paper/2205.14814/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Unsupervised 3D Pose Transfer with Cross Consistency and Dual Reconstruction](https://mlsanity.com/paper/2211.10278/) (2022)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)
- [Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics](https://mlsanity.com/paper/2202.10723/) (2022)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport](https://mlsanity.com/paper/2301.12721/) (2023)
- [Entropy Partial Transport with Tree Metrics: Theory and Practice](https://mlsanity.com/paper/2101.09756/) (2021)
- [Entropic Gromov-Wasserstein between Gaussian Distributions](https://mlsanity.com/paper/2108.10961/) (2021)
- [OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptation](https://mlsanity.com/paper/2205.10738/) (2022)
- [Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification](https://mlsanity.com/paper/2205.13573/) (2022)
- [A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2303.06595/) (2023)
- [Scalable Unbalanced Sobolev Transport for Measures on a Graph](https://mlsanity.com/paper/2302.12498/) (2023)
- [Semidefinite Relaxations of the Gromov-Wasserstein Distance](https://mlsanity.com/paper/2312.14572/) (2023)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [Online Learning to Transport via the Minimal Selection Principle](https://mlsanity.com/paper/2202.04732/) (2022)
- [Outlier-Robust Gromov-Wasserstein for Graph Data](https://mlsanity.com/paper/2302.04610/) (2023)
- [Geometry-Preserving Encoder/Decoder in Latent Generative Models](https://mlsanity.com/paper/2501.09876/) (2025)
- [Sliced Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2102.07115/) (2021)
- [Cycle Consistent Probability Divergences Across Different Spaces](https://mlsanity.com/paper/2111.11328/) (2021)
- [Personalised Federated Learning On Heterogeneous Feature Spaces](https://mlsanity.com/paper/2301.11447/) (2023)
- [Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space](https://mlsanity.com/paper/2310.11256/) (2023)
- [MoReL: Multi-omics Relational Learning](https://mlsanity.com/paper/2203.08149/) (2022)
- [Improving Generative Flow Networks with Path Regularization](https://mlsanity.com/paper/2209.15092/) (2022)

## Abstract (arXiv)

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.